We examine halo gas cross sections and covering fractions, fc , of intermediate-redshift Mg II absorption selected galaxies. We computed statistical absorber halo radii, Rx, using current values of dN/dz and Schechter luminosity function parameters, and have compared these values to the distribution of impact parameters and luminosities from a sample of 37 galaxies. For equivalent widths Wr(2796) ≥ 0.3 , we find 43 ≤ Rx ≤ 88 kpc, depending on the lower luminosity cutoff and the slope, β, of the Holmberg-like luminosity scaling, R Lβ. The observed distribution of impact parameters, D, are such that several absorbing galaxies lie at D>Rx and several non-absorbing galaxies lie at D < Rx. We deduced that fc must be less than unity and obtain a mean of 0.5 for our sample. Moreover, the data suggest that halo radii of Mg II absorbing galaxies do not follow a luminosity scaling with β in the range of 0.2-0.28, if fc = 1 as previously reported. However, provided fc 0.5, we find that halo radii can remain consistent with a Holmberg-like luminosity relation with β ≃ 0.2 and kpc. No luminosity scaling (β = 0) is also consistent with the observed distribution of impact parameters if fc ≤ 0.37. The data support a scenario in which gaseous halos are patchy and likely have non-symmetric geometric distributions about the galaxies. We suggest that halo gas distributions may not be governed primarily by galaxy mass/luminosity but also by stochastic processes local to the galaxy.